Abstract

Three-phase matrix converter-based dual AC to DC rectifier is reported in the literature. But these reports only indicate that dual DC output voltages with fixed value are possible by setting the desired AC output voltage phase angle leading by 30 degrees and output frequency zero in the model. Detailed modeling studies using SIMULINK reveal that with the frequency of desired AC output voltage set to zero, as the AC output voltage phase angle is varied from 0 to +\(\pi \) and 0 to \(-\pi \), dual DC output voltages in multitude of combinations are possible such as (a) both voltages positive and unequal, (b) both voltages positive and equal, (c) any one voltage zero and the other positive, (d) any one voltage positive and the other negative with unequal modulus value, (e) any one voltage positive and the other negative with equal modulus value, (f) any one voltage zero and the other negative, (g) both voltages negative and unequal, (h) both voltages negative and equal. This paper provides a detailed insight into this finding with a mathematical derivation for the dual DC output voltage magnitude. Theoretical finding is confirmed by model simulation.

Keywords

Appendix I

The model of the three-phase MC was developed in SIMULINK with cosine input and output voltages as defined in Eqs. 9 and 11. The three-phase source used is from the Electrical Source library in the SimPowerSystems blockset of SIMULINK. Here in the box corresponding to phase angle of phase A (degrees), a value of 90 is entered, with other boxes filled with appropriate values as used in the above model. The computed results obtained for various values of \(\varphi _{{O}}\) are tabulated in Table 1. The plot of \(v_{o1}\) and \(v_{o2}\) for a \(\varphi _{{O}}\) of +\(\pi \)/6 radians is shown in Fig. 6. Equations 23 and 24 are derived.

Three-phase output voltage in Eq. 11 is shown in Fig. 7. For any arbitrary angular frequency \(\omega _{O}\) of the output voltage, \(v_{ab}\) and \(v_{cb}\) which correspond to \(v_{o1}\) and \(v_{o2}\), lead \(v_a\) by \(\pi \)/6 and \(\pi \)/2 radians, respectively. Combining Eqs. 20 to 22 and noting the phase lead of \(v_{o1}\) and \(v_{o2}\) with respect to \(v_a\) and \(\omega _{0}\) zero, Eqs. 23 and 24 follow.

Appendix II

Consider the output voltage defined in Eq. 11 for any arbitrary angular frequency \(\omega _{{O}}\) rad/s. This is shown in Fig. 8. Now both the three-phase input and output voltages are given an intentional phase lag of \(\pi \)/2 radians considering practical implementation. The output voltages are measured across output phase a–b and c–b. The initial position of \(v_{ab}\) and \(v_{cb}\) is shown in Fig. 8. When the output voltage of each phase lags by \(\pi \)/2 radians, the new position of \(v_{ab}\) and \(v_{cb}\) marked \(v_{ab}^\prime \) and \(v_{cb}^\prime \) is shown in Fig. 8. \(v_{ab}^\prime \) is along the line of \(v_c\) lagging \(v_a\) by \(\pi \)/3 radians, and \(v_{cb}^\prime \) is along the line and in phase with \(v_a\). \(v_{ab}^\prime \) and \(v_{cb}^\prime \) correspond to \(v_{o1}\) and \(v_{o2}\), respectively. Combining Eqs. 20 to 22 and noting the phase lag of \(v_{o1}\) and \(v_{o2}\) with respect to \(v_a\) and \(\omega _{{o}}\) zero, Eqs. 25 and 26 follow.